Fast multipole acceleration of the MEG/EEG boundary element method

Area of Science:

• Computational physics
• Biomedical engineering
• Numerical methods

Background:

• Accurate forward electrostatic problem solutions are crucial for magneto- and electroencephalography (MEG/EEG) inverse problem analysis.
• The standard symmetric Galerkin boundary element method (BEM) offers accuracy but faces computational and memory limitations for large-scale applications.

Purpose of the Study:

• To develop and evaluate a computationally efficient acceleration technique for the symmetric Galerkin boundary element method (BEM).
• To enable the accurate and efficient solution of forward electrostatic problems in the context of MEG/EEG analysis for large datasets.

Main Methods:

• Implementation of a fast multipole-based acceleration for the symmetric boundary element method (BEM).
• Development of a hierarchical data structure for BEM elements.
• Approximation of long-range interactions using spherical harmonics expansions.

Main Results:

• The accelerated BEM achieves accuracy comparable to the direct symmetric Galerkin BEM.
• For large-scale problems, the fast multipole-accelerated BEM demonstrates significant improvements in speed.
• The new method offers substantial reductions in memory consumption compared to the direct BEM for large problems.

Conclusions:

• The fast multipole-accelerated BEM provides an accurate, faster, and more memory-economical solution for forward electrostatic problems.
• This advancement is particularly beneficial for computationally demanding applications like large-scale MEG/EEG analysis.
• The method overcomes the limitations of traditional BEM, enhancing its applicability in neuroimaging and other fields.